Practical Foundations of Mathematics

Practical Foundations of Mathematics

Practical Foundations of Mathematics, by Paul Taylor, explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science.

Description

In addition to the formal logic, this volume examines the relationship between computer languages and “plain English” mathematical proofs. The book introduces the reader to discrete mathematics, reasoning, and categorical logic. It offers a new approach to term algebras, induction and recursion and proves in detail the equivalence of types and categories. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries across universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.

Table of Contents

  • First Order Reasoning
  • Types and Induction
  • Posets and Lattices
  • Cartesian Closed Categories
  • Limits and Colimits
  • Structural Recursion
  • Adjunctions
  • Algebra with Dependent Types
  • The Quantifiers

Book Details

Author(s): Paul Taylor
Publisher: Cambridge University Press
Format(s): HTML(Online)
Number of pages: 588
Link: Read online.







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